$1+\dfrac{1}{2^{10}}+\dfrac{1}{3^{10}}+\dfrac{1}{4^{10}}+...+\dfrac{1}{n^{10}}+...$ Is the series convergent or divergent? Choose 1 answer: Choose 1 answer: (Choice A) A Convergent (Choice B) B Divergent
Solution: This is a $p$ -series, because it's of the general form $\sum\limits_{n=1}^{\infty}\dfrac{1}{n^{^p}}$. Specifically, this is a $p$ -series where $p=10$. $p$ -series are convergent for $p>1$ and divergent for $0<p\leq1$. [What about non-positive p-values?] In conclusion, the series is convergent.